JEE Main 2021MathematicsBinomial TheoremMediumMCQ

JEE Main 2021 — Binomial Theorem Question with Solution

JEE Main 2021 (26 Aug Shift 1)

Question

If Cr20 is the co-efficient of xr in the expansion of (1+x)20, then the value of ∑r=020r2Cr20 is equal to:

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Show full solutionCorrect option: A
Correct answer
A420×218

Step-by-step explanation

∑r=020r2Cr20=∑rr·Cr20=∑r=120r·20.Cr-119

⇒20∑r=120(r-1+1)·19Cr-1=20∑r=120(r-1)·19Cr-1+∑r=120Cr-119

⇒2019∑r=220Cr-218+∑r=120Cr-119

⇒(380)218+20·219⇒220·(95+10)=(105)220=420×218

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About this question

This is a previous-year question from JEE Main 2021, covering the Binomial Theorem chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.